Sketching the plane curve r(t) = <cos(t), sin(t)>

[mr_coffee]

Hello everyone, I'm confused on this problem. It says (a) sketch the plane curve with the given vector equatiion. (b) find r'(t) which is easy. (c)Sketch the position vector r(t) and the tagent vector r'(t) for the given value of t.

r(t) = <cos t, sin t>, t = PI/4;
I got part b of course. But I'm stuck on how they they got part a and c. How did they get a circle, and how did they know the circle is going counter clock wise? Thanks. Here is my work:
http://img134.imageshack.us/img134/8246/w00ta0qt.jpg

 

[arildno]

As for a), what is $x(t)^{2}+y(t)^{2}$?
As for c), what is $\vec{r}(\frac{\pi}{4})$ and [itex]\frac{d\vec{r}}{dt}(\frac{\pi}{4})[/tex]?[/itex]